{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T04:28:23Z","timestamp":1778128103100,"version":"3.51.4"},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642010002","type":"print"},{"value":"9783642010019","type":"electronic"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-01001-9_2","type":"book-chapter","created":{"date-parts":[[2009,4,15]],"date-time":"2009-04-15T08:38:25Z","timestamp":1239784705000},"page":"36-53","source":"Crossref","is-referenced-by-count":53,"title":["Breaking RSA Generically Is Equivalent to Factoring"],"prefix":"10.1007","author":[{"given":"Divesh","family":"Aggarwal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ueli","family":"Maurer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"2_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1007\/3-540-69053-0_33","volume-title":"Advances in Cryptology - EUROCRYPT \u201997","author":"N. Bari\u0107","year":"1997","unstructured":"Bari\u0107, N., Pfitzmann, B.: Collision-free accumulators and fail-stop signature schemes without trees. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol.\u00a01233, pp. 480\u2013494. Springer, Heidelberg (1997)"},{"key":"2_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/3-540-68697-5_22","volume-title":"Advances in Cryptology - CRYPTO \u201996","author":"D. Boneh","year":"1996","unstructured":"Boneh, D., Lipton, R.: Black box fields and their application to cryptography. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol.\u00a01109, pp. 283\u2013297. Springer, Heidelberg (1996)"},{"key":"2_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/BFb0054117","volume-title":"Advances in Cryptology - EUROCRYPT \u201998","author":"D. Boneh","year":"1998","unstructured":"Boneh, D., Venkatesan, R.: Breaking RSA may not be equivalent to factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol.\u00a01403, pp. 59\u201371. Springer, Heidelberg (1998)"},{"key":"2_CR4","unstructured":"Brown, D.R.L.: Breaking RSA may be as difficult as factoring. In: Cryptology ePrint Archive, Report 205\/380 (2006)"},{"key":"2_CR5","volume-title":"A concrete introduction to higher algebra","author":"L. Childs","year":"1992","unstructured":"Childs, L.: A concrete introduction to higher algebra. Springer, New York (1992)"},{"key":"2_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/BFb0055717","volume-title":"Advances in Cryptology - CRYPTO \u201998","author":"R. Cramer","year":"1998","unstructured":"Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol.\u00a01462, pp. 13\u201325. Springer, Heidelberg (1998)"},{"key":"2_CR7","doi-asserted-by":"crossref","unstructured":"Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. In: 6th ACM Conference on Computer and Communications Security, pp. 46\u201352 (1999)","DOI":"10.1145\/319709.319716"},{"key":"2_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/3-540-46035-7_17","volume-title":"Advances in Cryptology - EUROCRYPT 2002","author":"I.B. Damg\u00e5rd","year":"2002","unstructured":"Damg\u00e5rd, I.B., Koprowski, M.: Generic lower bounds for root extraction and signature schemes in general groups. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol.\u00a02332, pp. 256\u2013271. Springer, Heidelberg (2002)"},{"issue":"6","key":"2_CR9","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W. Diffie","year":"1976","unstructured":"Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory\u00a022(6), 644\u2013654 (1976)","journal-title":"IEEE Transactions on Information Theory"},{"key":"2_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1007\/BFb0052225","volume-title":"Advances in Cryptology - CRYPTO \u201997","author":"E. Fujisaki","year":"1997","unstructured":"Fujisaki, E., Okamoto, T.: Statistical zero knowledge protocols to prove modular polynomial relations. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol.\u00a01294, pp. 16\u201330. Springer, Heidelberg (1997)"},{"key":"2_CR11","unstructured":"Jager, T.: Generic group algorithms. Master\u2019s thesis, Ruhr Universit\u00e4t Bochum (2007)"},{"key":"2_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/978-3-540-76900-2_2","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2007","author":"A. Joux","year":"2007","unstructured":"Joux, A., Naccache, D., Thom\u00e9, E.: When e-th roots become easier than factoring. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol.\u00a04833, pp. 13\u201328. Springer, Heidelberg (2007)"},{"key":"2_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/11935230_16","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2006","author":"G. Leander","year":"2006","unstructured":"Leander, G., Rupp, A.: On the equivalence of RSA and factoring regarding generic ring algorithms. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol.\u00a04284, pp. 241\u2013251. Springer, Heidelberg (2006)"},{"key":"2_CR14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139172769","volume-title":"Introduction to finite fields and their applications","author":"R. Lidl","year":"1994","unstructured":"Lidl, R., Niederreiter, H.: Introduction to finite fields and their applications. Cambridge University Press, Cambridge (1994)"},{"key":"2_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/3-540-48658-5_26","volume-title":"Advances in Cryptology - CRYPTO \u201994","author":"U. Maurer","year":"1994","unstructured":"Maurer, U.: Towards the equivalence of breaking the diffie-hellman protocol and computing discrete logarithms. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol.\u00a0839, pp. 271\u2013281. Springer, Heidelberg (1994)"},{"issue":"3","key":"2_CR16","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/BF00202269","volume":"8","author":"U. Maurer","year":"1995","unstructured":"Maurer, U.: Fast generation of prime numbers and secure public-key cryptographic parameters. Journal of Cryptology\u00a08(3), 123\u2013155 (1995)","journal-title":"Journal of Cryptology"},{"key":"2_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/11586821_1","volume-title":"Cryptography and Coding","author":"U. Maurer","year":"2005","unstructured":"Maurer, U.: Abstract models of computation in cryptography. In: Smart, N.P. (ed.) Cryptography and Coding 2005. LNCS, vol.\u00a03796, pp. 1\u201312. Springer, Heidelberg (2005)"},{"issue":"5","key":"2_CR18","doi-asserted-by":"publisher","first-page":"1689","DOI":"10.1137\/S0097539796302749","volume":"28","author":"U. Maurer","year":"1999","unstructured":"Maurer, U., Wolf, S.: The relationship between breaking the Diffie-Hellman protocol and computing discrete logarithms. SIAM Journal of Computing\u00a028(5), 1689\u20131721 (1999)","journal-title":"SIAM Journal of Computing"},{"key":"2_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/11426639_23","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2005","author":"D. Micciancio","year":"2005","unstructured":"Micciancio, D.: The RSA group is pseudo-free. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol.\u00a03494, pp. 387\u2013403. Springer, Heidelberg (2005)"},{"issue":"2","key":"2_CR20","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/BF02113297","volume":"55","author":"V.I. Nechaev","year":"1994","unstructured":"Nechaev, V.I.: Complexity of a deterministic algorithm for the discrete logarithm. Mathematical Notes\u00a055(2), 91\u2013101 (1994)","journal-title":"Mathematical Notes"},{"key":"2_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1007\/978-3-540-24638-1_28","volume-title":"Theory of Cryptography","author":"R.L. Rivest","year":"2004","unstructured":"Rivest, R.L.: On the notion of pseudo-free groups. In: Naor, M. (ed.) TCC 2004. LNCS, vol.\u00a02951, pp. 505\u2013521. Springer, Heidelberg (2004)"},{"key":"2_CR22","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R. Rivest","year":"1978","unstructured":"Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM\u00a021, 120\u2013126 (1978)","journal-title":"Communications of the ACM"},{"key":"2_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/3-540-69053-0_18","volume-title":"Advances in Cryptology - EUROCRYPT \u201997","author":"V. Shoup","year":"1997","unstructured":"Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol.\u00a01233, pp. 256\u2013266. Springer, Heidelberg (1997)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology - EUROCRYPT 2009"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-01001-9_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T09:38:06Z","timestamp":1551951486000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-01001-9_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642010002","9783642010019"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-01001-9_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009]]}}}